Skills Practice Skills Practice for Lesson 3.1

Transcription

1 Skills Practice Skills Practice for Lesson.1 Name ate onstellations Naming, Measuring, and lassifying ngles Vocabulary Write the term from the box that best completes each statement. point line segment straight angle endpoints line sides right angle initial point ray vertex acute angle congruent angles angle degree obtuse angle measure of an angle 1. One unit of measure for angles is a(n). 2. (n) is an angle that has a measure of 90º.. (n) is made up of points that extend infinitely in two opposite dimensions. 4. ngles that have the same measure are. 5. (n) is an angle that has a measure greater than 0º and less than 90º. 6. (n) is a portion of a line between two points, called the endpoints. 7. The of a segment are the points at which the segment ends. 8. n angle that has a measure greater than 90º and less than 180º is a(n). 9. (n) consists of a point P on a straight line and all points on the line to one side of P. 10. The rays of an angle are the of the angle. 11. (n) has no dimension, indicates a specific position in space, and it is usually represented by a small dot. 12. The indicates the size of the angle. 1. The of an angle is the point where the two rays forming the angle intersect. 14. figure formed by two rays that extend from a common point called the vertex is a(n). 15. (n) is the point at which a ray begins. 16. (n) is an angle that has a measure of 180º. hapter Skills Practice 7

2 Problem Set Identify all possible names for each figure using words and using symbols G H 21. I 22. L M J K N 2. O P 24. Q R 74 hapter Skills Practice

3 Name ate lassify each angle as acute, right, obtuse, or straight G L H I J K 29. M N O 0. Q R P Measure each angle using a protractor.. What is the measure of? 4. What is the measure of? hapter Skills Practice 75

4 76 hapter Skills Practice 5. What is the measure of HGI? 6. What is the measure of JKL? H G I J K L 7. What is the measure of ORM? 8. What is the measure of SXU? R M Q P O N X S W V U T etermine whether the angles are congruent. xplain your answer L K H G I J

5 Name ate 41. O N L M P Q 42. T U R S V W Measure the three angles of each triangle using a protractor. Then classify each angle as acute, right, obtuse, or straight hapter Skills Practice 77

6 78 hapter Skills Practice

7 Skills Practice Skills Practice for Lesson.2 Name ate able-stayed ridges Special ngles Vocabulary Match each definition to its corresponding term. 1. ngles whose sides form two pairs of opposite rays a. adjacent angles 2. Two angles whose measures sum to 180º b. supplementary angles. Two adjacent angles that have non-common sides c. complementary angles that are opposite rays 4. ngles that share a common side and a common d. vertical angles vertex and lie on opposite sides of their common side 5. Two rays on the same line that have the same e. opposite rays initial point and extend in opposite directions 6. Two angles whose measures sum to 90º f. linear pair Problem Set Identify all pairs of adjacent angles in each figure G I J K L H M N hapter Skills Practice 79

8 Q R S T U V W P O X Identify all pairs of complementary angles in each figure G H 20 I 1. K L J M O N 80 hapter Skills Practice

9 Name ate 14. R S P Q T Identify all pairs of supplementary angles in each figure G J I H hapter Skills Practice 81

10 17. K L N O M 18. P Q S T 80 R Identify all pairs of vertical angles in each figure I J H G 82 hapter Skills Practice

11 Name ate K T Q O L U N M S R Identify all pairs of angles that form linear pairs in each figure I J G H 25. K O L M N 26. S P T R Q hapter Skills Practice 8

12 Identify all possible classifications of each pair of angles (adjacent, complementary, supplementary, vertical, or linear pair). 27. Identify all possible classifications for and. 28. Identify all possible classifications for GJH and HJI. G H J I 29. Identify all possible classifications for KOL and LOM. K L O N M 0. Identify all possible classifications for QTR and RTS. R Q P T S 84 hapter Skills Practice

13 Name ate 1. Identify all possible classifications for VYU and XYW. V U Y W X 2. Identify all possible classifications for and. alculate the measure of the indicated angle.. If the measure of is 77º and is complementary to, what is the measure of? 4. If the measure of GHI is 56º and JKL is complementary to GHI, what is the measure of JKL? 5. If the measure of MNO is 6º and PQR is complementary to MNO, what is the measure of PQR? hapter Skills Practice 85

14 6. If the measure of STU is 89º and VWX is complementary to STU, what is the measure of VWX? 7. If the measure of is 6º and is supplementary to, what is the measure of? 8. If the measure of GHI is 45º and JKL is supplementary to GHI, what is the measure of JKL? 9. If the measure of MNO is 5º and PQR is supplementary to MNO, what is the measure of PQR? 40. If the measure of STU is 82º and VWX is supplementary to STU, what is the measure of VWX? 86 hapter Skills Practice

15 Skills Practice Skills Practice for Lesson. Name ate esigning a Kitchen ngles of a Triangle Vocabulary efine each term using your own words. 1. interior angle 2. exterior angle. theorem 4. proof Problem Set Identify all possible names for each triangle G 8. J H K I L hapter Skills Practice 87

16 Measure the three angles of each triangle using a protractor. Then calculate the sum of the measures of the three angles G H I 12. J 1. M L K O N 88 hapter Skills Practice

17 Name ate 14. P Q R alculate the measure of each angle. 15. What is the measure of? 5 90? 16. What is the measure of?? hapter Skills Practice 89

18 17. What is the measure of G? G? 12 H 24 I 18. What is the measure of L? J 57 9 K? L alculate the measure of each angle. 19. What is the measure of? 20. What is the measure of G? 45 98? 2 71? G 90 hapter Skills Practice

19 Name ate 21. What is the measure of GIJ? 22. What is the measure of JLM? G J? 28 J I H 26? 19 M L K Measure each exterior angle and its two nonadjacent interior angles using a protractor. Then, describe the measure of the exterior angle with respect to each nonadjacent interior angle G hapter Skills Practice 91

20 25. G I J H 26. J K L M 92 hapter Skills Practice

21 Skills Practice Skills Practice for Lesson.4 Name ate Origami lassifying Triangles Vocabulary Identify which triangle each term describes. G H I 1. acute triangle 2. right triangle. obtuse triangle 4. equiangular triangle 5. equilateral triangle 6. isosceles triangle 7. scalene triangle Problem Set lassify each triangle as equilateral, isosceles, or scalene hapter Skills Practice 9

22 lassify each triangle as equilateral, isosceles, or scalene. xplain your answer. 14. Triangle has sides with the following lengths: is 8 cm long, is 6 cm long, and is 5 cm long. What kind of triangle is? 15. Triangle has sides with the following lengths: is 9 inches long, is 10 inches long, and is 8 inches long. What kind of triangle is? 16. Triangle GHI has sides with the following lengths: GH is 12 mm long, HI is 12 mm long, and IG is 12 mm long. What kind of triangle is GHI? 17. Triangle JKL has sides with the following lengths: JK is 21 cm long, KL is 21 cm long, and JL is 21 cm long. What kind of triangle is JKL? 18. Triangle MNO has sides with the following lengths: MN is 22 feet long, ON is 1 feet long, and OM is 1 feet long. What kind of triangle is MNO? 94 hapter Skills Practice

23 Name ate 19. Triangle PQR has sides with the following lengths: PQ is 17 in. long, QR is 25 in. long, and RP is 17 in. long. What kind of triangle is PQR? lassify each triangle as acute, right, or obtuse lassify each triangle as acute, right, or obtuse. xplain your answer. 26. Triangle has angles with the following measures: m 17º, m 90º, and m 7º. What kind of triangle is? 27. Triangle has angles with the following measures: m 52º, m 8º, and m 90º. What kind of triangle is? hapter Skills Practice 95

24 28. Triangle GHI has angles with the following measures: m G 154º, m H 1º, and m I 1º. What kind of triangle is GHI? 29. Triangle JKL has angles with the following measures: m J 46º, m K 5º, and m L 99º. What kind of triangle is JKL? 0. Triangle MNO has angles with the following measures: m M 87º, m N 25º, and m O 68º. What kind of triangle is MNO? 1. Triangle PQR has angles with the following measures: m P 59º, m Q 71º, and m R 50º. What kind of triangle is PQR? lassify each triangle with respect to its sides and angles hapter Skills Practice

25 Name ate 4. G H I 5. J K L 6. M N O 7. P Q R hapter Skills Practice 97

26 98 hapter Skills Practice

27 Skills Practice Skills Practice for Lesson.5 Name ate Work in onstruction uplicating ngles, uplicating Line Segments, and onstructing Perpendiculars Vocabulary Write the term from the box that best completes each statement. construct a perpendicular interior altitude of a triangle exterior altitude of a triangle duplicate equilateral triangle 1. (n) is a perpendicular segment that indicates the height of a triangle. It is drawn from a vertex outside the triangle to the line containing the opposite side of the triangle. 2. (n) is a triangle that has all three sides equal.. When you, you use a compass and straightedge to create a line or segment that is exactly perpendicular to the original figure. 4. To a figure, use a compass and straight edge or patty paper to create an exact copy of the figure. 5. (n) is a perpendicular segment that indicates the height of a triangle. It is drawn from a vertex to the opposite side of the triangle. Problem Set Use a compass and a straightedge to duplicate each line segment hapter Skills Practice 99

28 Use patty paper to duplicate each line segment Use a compass and a straightedge to duplicate each angle Use patty paper to duplicate each angle hapter Skills Practice

29 Name ate Use a compass and a straightedge to construct a perpendicular to the given line or ray Use patty paper to construct a perpendicular to the given line or ray onstruct an equilateral triangle given one side of the triangle hapter Skills Practice 101

30 onstruct an altitude of the given triangle. 4. onstruct an interior altitude to the triangle that intersects vertex. 5. onstruct an interior altitude to the triangle that intersects vertex. 6. onstruct an exterior altitude to the triangle that intersects vertex G. G H I 7. onstruct an exterior altitude to the triangle that intersects vertex J. J K L 102 hapter Skills Practice

31 Skills Practice Skills Practice for Lesson.6 Name ate uilding a Shed Triangle Inequality Theorems and Hinge Theorem Vocabulary efine each term using your own words. 1. Triangle Inequality 2. duplicate an angle. construct a perpendicular 4. Hinge Theorem hapter Skills Practice 10

32 Problem Set Write an inequality that expresses the possible length of the unknown side. 5. What could be the length of? 6. What could be the length of? 10 m 6 cm 8 m 9 cm 7. What could be the length of HI? 20 in. I 8. What could be the length of JL? 12 ft J H 14 in. G K 7 ft L 9. What could be the length of MN? 10. What could be the length of QR? M P N 11 cm O cm 9 mm 1 mm R Q 104 hapter Skills Practice

33 Name ate Without measuring the angles or sides, list the angles in order from least to greatest. Then list the side lengths in order from least to greatest G H 14. J 18 I K L 15. M 5 ft N 7 ft ft O 16. Q.1 m P 5.4 m 5.8 m R 17. S 9 in. U 1 in. 12 in. T cm W 25 cm 2 cm V X hapter Skills Practice 105

34 Using a protractor and ruler, determine the relationship between the sides and the angles of each triangle Identify the shortest side and the smallest angle of the triangle. What is the relationship between them? 20. Identify the longest side and the greatest angle of the triangle. What is the relationship between them? 21. Identify the greatest angle and the two shorter sides of the triangle. What is the relationship between them? G I H 22. Identify the smallest angle and the two longer sides of the triangle. What is the relationship between them? J L K 106 hapter Skills Practice

35 Name ate Given two triangles, use the Hinge Theorem to compare the lengths of their unknown sides. 2. If the measure of is 45º and the measure of is 60º, compare the lengths of the unknown sides. 24. If the measure of is 90º and the measure of is 75º, compare the lengths of the unknown sides. 25. If the measure of is 124º and the measure of is 108º, compare the lengths of the unknown sides. hapter Skills Practice 107

36 26. If the measure of is 115º and the measure of is 15º, compare the lengths of the unknown sides. 27. ompare the lengths of the unknown sides ompare the lengths of the unknown sides hapter Skills Practice

37 Name ate 29. If the measure of is 12º and the measure of is 104º, compare the lengths of the unknown sides. 0. If the measure of is 77º and the measure of is 6º, compare the lengths of the unknown sides. 1. If the measure of is 44º and the measure of is 22º, compare the lengths of the unknown sides. hapter Skills Practice 109

38 2. If the measure of is 18º and the measure of is 4º, compare the lengths of the unknown sides. 110 hapter Skills Practice